In this manuscript, we mainly investigate the topological pressure for iterated function systems on a compact metric space defined by Wang and Liao [Dynam. Syst., 2021, 36(3): 483–506]. Given a factor map, we establish a formula of topological pressure of a factor map, which generalizes Bowen's inequality in [Trans. Amer. Math. Soc., 1971,153: 401–414.] to iterated function systems. Consequently, we further study the power rule of a topological pressure for iterated function systems.